Finite Group Databasebeta

← C149×#11083 #49190032

Subgroups — C149×#11083 #49190032

Order 38144.

974 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#421×C149C211yesmaximal, characteristic
2#2896×C149C211yesmaximal, characteristic
3#2297×C149C211yesmaximal, characteristic
4#2296×C149C211yesmaximal, characteristic, complemented
5#1733×C149C211yesmaximal, characteristic, complemented
6C2×H(3,ℤ/4)×C149C211yesmaximal, characteristic, complemented
7#1728×C149C211yesmaximal, characteristic, complemented
8C22×#41×C149C2211yescharacteristic
9C22×M16×C149C2211yescharacteristic
10C22×M16×C149C2211yescharacteristic
11C2×#117×C149C2211yescharacteristic
12C2×#117×C149C2211yescharacteristic
13C2×#117×C149C2211yescharacteristic
14C22×C42×C149C2211yescharacteristic
15#421×C149—22no—
16#421×C149C414yescomplemented
17C2×#104×C149—22no—
18#419×C149—21no—
19#418×C149—21no—
20#417×C149—22no—
21#416×C149—22no—
22#391×C149—21no—
23#390×C149—21no—
24#389×C149—22no—
25#386×C149—22no—
26#385×C149—22no—
27C4×C4⋊C4×C149—22no—
28C4×C22⋊C4×C149—22no—
29#339×C149—22no—
30H(3,ℤ/4)×C149—22no—
31#336×C149—22no—
32C2×#41×C149—21no—
33C2×#41×C149—21no—
34C2×#41×C149—21no—
35C2×#41×C149—21no—
36C2×#41×C149—21no—
37C2×#41×C149—21no—
38C2×#41×C149—21no—
39C2×#41×C149—21no—
40C2×#41×C149—21no—
41C2×#41×C149—21no—
42C2×#41×C149C2×C412yes—
43C2×#41×C149Q812yes—
44C22×Q8×C149D411yescharacteristic
45C22×D4×C149—21no—
46C22×D4×C149D411yescharacteristic
47C23×C4×C149—21no—
48C23×C4×C149D412yes—
49C23×C4×C149C2311yescharacteristic
50C2×M16×C149—21no—
51C2×M16×C149—21no—
52C2×M16×C149—21no—
53C2×M16×C149—21no—
54C2×M16×C149—21no—
55C2×M16×C149—21no—
56C2×M16×C149—21no—
57C2×M16×C149—21no—
58C2×M16×C149—21no—
59C2×M16×C149—21no—
60C2×M16×C149—21no—
61C2×M16×C149C2×C412yes—
62C22×C8×C149—21no—
63C22×C8×C149D412yes—
64#117×C149—21no—
65#117×C149—21no—
66#117×C149—21no—
67#117×C149—21no—
68#117×C149—21no—
69#117×C149—21no—
70#117×C149—21no—
71#117×C149—21no—
72#117×C149—21no—
73#117×C149—21no—
74#117×C149C2×C412yes—
75#117×C149D412yes—
76C2×C4⋊C4×C149—21no—
77C2×C4⋊C4×C149—24no—
78C2×C4⋊C4×C149—21no—
79C2×C4⋊C4×C149D412yes—
80C2×C22⋊C4×C149—21no—
81C2×C22⋊C4×C149—24no—
82C2×C22⋊C4×C149—21no—
83C2×C22⋊C4×C149—21no—
84C2×C42×C149—21no—
85C2×C42×C149—21no—
86C2×C42×C149—21no—
87C2×C42×C149—21no—
88C2×C42×C149—21no—
89C2×C42×C149—21no—
90C2×C42×C149—21no—
91C2×C42×C149D412yes—
92C2×C42×C149D412yes—
93#104×C149—28no—
94#103×C149—24no—
95#102×C149—24no—
96#95×C149—24no—
97#95×C149—24no—
98C24×C149—21no—
99C24×C149C2×D411yescharacteristic
100#41×C149—22no—
101#41×C149—22no—
102#41×C149—22no—
103#41×C149—22no—
104#41×C149—22no—
105#41×C149—22no—
106#41×C149—22no—
107#41×C149—22no—
108#41×C149—41no—
109#41×C149—41no—
110#41×C149—41no—
111#41×C149—41no—
112#41×C149—41no—
113#41×C149—41no—
114#41×C149—41no—
115#41×C149—41no—
116C2×Q8×C149—21no—
117C2×Q8×C149—21no—
118C2×Q8×C149—21no—
119C2×Q8×C149—21no—
120C2×Q8×C149—21no—
121C2×Q8×C149C4⋊C412yescomplemented
122C2×D4×C149—22no—
123C2×D4×C149—22no—
124C2×D4×C149—21no—
125C2×D4×C149—21no—
126C2×D4×C149—21no—
127C2×D4×C149—21no—
128C2×D4×C149—21no—
129C2×D4×C149—41no—
130C2×D4×C149—41no—
131C2×D4×C149—41no—
132C2×D4×C149—41no—
133C2×D4×C149C4⋊C412yescomplemented
134C22×C4×C149—21no—
135C22×C4×C149—22no—
136C22×C4×C149—22no—
137C22×C4×C149—22no—
138C22×C4×C149—22no—
139C22×C4×C149—22no—
140C22×C4×C149—22no—
141C22×C4×C149—22no—
142C22×C4×C149—22no—
143C22×C4×C149—44no—
144C22×C4×C149—41no—
145C22×C4×C149—41no—
146C22×C4×C149—41no—
147C22×C4×C149—41no—
148C22×C4×C149C22×C411yescharacteristic
149C22×C4×C149C2×D411yescharacteristic
150C22×C4×C149C2×D411yescharacteristic
151C22×C4×C149C2×D411yescharacteristic
152C22×C4×C149C2×D411yescharacteristic
153C22×C4×C149C2×D411yescharacteristic
154C22×C4×C149C2×D411yescharacteristic
155C22×C4×C149C2×Q811yescharacteristic
156C22×C4×C149#4111yescharacteristic
157C22×C4×C149#4111yescharacteristic
158C22×C4×C149#4111yescharacteristic
159C22×C4×C149#4111yescharacteristic
160C22×C4×C149#4111yescharacteristic
161C22×C4×C149#4111yescharacteristic
162M16×C149—22no—
163M16×C149—22no—
164M16×C149—41no—
165M16×C149—41no—
166M16×C149—41no—
167M16×C149—41no—
168M16×C149—41no—
169M16×C149—41no—
170C2×C8×C149—22no—
171C2×C8×C149—22no—
172C2×C8×C149—22no—
173C2×C8×C149—22no—
174C2×C8×C149—41no—
175C2×C8×C149—41no—
176C4⋊C4×C149—22no—
177C4⋊C4×C149—22no—
178C4⋊C4×C149—22no—
179C4⋊C4×C149—22no—
180C4⋊C4×C149—48no—
181C4⋊C4×C149—41no—
182C4⋊C4×C149—41no—
183C22⋊C4×C149—22no—
184C22⋊C4×C149—22no—
185C22⋊C4×C149—48no—
186C22⋊C4×C149—41no—
187C22⋊C4×C149—41no—
188C22⋊C4×C149—41no—
189C22⋊C4×C149—41no—
190C42×C149—22no—
191C42×C149—22no—
192C42×C149—22no—
193C42×C149—41no—
194C42×C149—41no—
195C42×C149—41no—
196C42×C149—41no—
197C42×C149—41no—
198C42×C149—41no—
199C42×C149C22⋊C414yescomplemented
200C23×C149—22no—
201C23×C149—42no—
202C23×C149—44no—
203C23×C149—41no—
204C23×C149—41no—
205C23×C149C4×D411yescharacteristic
206C23×C149#12011yescharacteristic
207C23×C149#12011yescharacteristic
208C23×C149#12111yescharacteristic
209C23×C149#12111yescharacteristic
210C23×C149C22⋊Q811yescharacteristic
211C23×C149#12411yescharacteristic
212Q8×C149—22no—
213Q8×C149—22no—
214Q8×C149—41no—
215Q8×C149—41no—
216D4×C149—22no—
217D4×C149—22no—
218D4×C149—42no—
219D4×C149—42no—
220D4×C149—42no—
221D4×C149—42no—
222D4×C149—41no—
223D4×C149—41no—
224C2×C4×C149—24no—
225C2×C4×C149—24no—
226C2×C4×C149—24no—
227C2×C4×C149—22no—
228C2×C4×C149—24no—
229C2×C4×C149—44no—
230C2×C4×C149—42no—
231C2×C4×C149—42no—
232C2×C4×C149—42no—
233C2×C4×C149—42no—
234C2×C4×C149—41no—
235C2×C4×C149—41no—
236C2×C4×C149—42no—
237C2×C4×C149—42no—
238C2×C4×C149—42no—
239C2×C4×C149—42no—
240C2×C4×C149—44no—
241C2×C4×C149—44no—
242C2×C4×C149—42no—
243C2×C4×C149—42no—
244C2×C4×C149C2×C22⋊C411yescharacteristic
245C2×C4×C149C2×C4⋊C411yescharacteristic
246C2×C4×C149#11711yescharacteristic
247C2×C4×C149C4×D411yescharacteristic
248C2×C4×C149C4×D411yescharacteristic
249C2×C4×C149C4×D411yescharacteristic
250C2×C4×C149#12011yescharacteristic
251C2×C4×C149#12111yescharacteristic
252C2×C4×C149#12111yescharacteristic
253C2×C4×C149#12111yescharacteristic
254C2×C4×C149#12111yescharacteristic
255C2×C4×C149#12111yescharacteristic
256C2×C4×C149#12111yescharacteristic
257C2×C4×C149C22⋊Q811yescharacteristic
258C2×C4×C149C22⋊Q811yescharacteristic
259C2×C4×C149C22⋊Q811yescharacteristic
260C2×C4×C149C22⋊Q811yescharacteristic
261C2×C4×C149C22⋊Q811yescharacteristic
262C2×C4×C149#12311yescharacteristic
263C2×C4×C149#12311yescharacteristic
264C2×C4×C149#12311yescharacteristic
265C2×C4×C149#12311yescharacteristic
266C2×C4×C149#12311yescharacteristic
267C2×C4×C149#12411yescharacteristic
268C2×C4×C149#12411yescharacteristic
269C2×C4×C149#12611yescharacteristic
270C2×C4×C149#12611yescharacteristic
271C2×C4×C149#12711yescharacteristic
272C8×C149—42no—
273C8×C149—42no—
274C22×C149—22no—
275C22×C149—22no—
276C22×C149—22no—
277C22×C149—41no—
278C22×C149—41no—
279C22×C149—41no—
280C22×C149—41no—
281C22×C149—44no—
282C22×C149—42no—
283C22×C149—82no—
284C22×C149—82no—
285C22×C149#38511yescharacteristic
286C22×C149#38611yescharacteristic
287C22×C149#38811yescharacteristic
288C22×C149#39211yescharacteristic
289C22×C149#39311yescharacteristic
290C22×C149#39411yescharacteristic
291C22×C149#39611yescharacteristic
292C4×C149—44no—
293C4×C149—42no—
294C4×C149—44no—
295C4×C149—82no—
296C4×C149—82no—
297C4×C149#38011yescharacteristic
298C4×C149#38511yescharacteristic
299C4×C149#38811yescharacteristic
300C4×C149#39011yescharacteristic
301C4×C149#39411yescharacteristic
302C4×C149#39611yescharacteristic
303C4×C149#39711yescharacteristic
304C4×C149#39911yescharacteristic
305C2×C149—21no—
306C2×C149—21no—
307C2×C149—21no—
308C2×C149—21no—
309C2×C149—21no—
310C2×C149—21no—
311C2×C149—82no—
312C2×C149#143911yescharacteristic
313C2×C149#201012yes—
314#11083C14911yesmaximal, characteristic, direct product factor, Sylow
315C149#1108311yescharacteristic, direct product factor, Sylow
316C2×#421C2×C14911yescharacteristic
317#2896C2×C14911yescharacteristic
318#2297C2×C14911yescharacteristic
319#2296C2×C14911yescharacteristic, complemented
320#1733C2×C14911yescharacteristic, complemented
321C2×H(3,ℤ/4)C2×C14911yescharacteristic, complemented
322#1728C2×C14911yescharacteristic, complemented
323C22×#41C22×C14911yescharacteristic
324C22×M16C22×C14911yescharacteristic
325C22×M16C22×C14911yescharacteristic
326C2×#117C22×C14911yescharacteristic
327C2×#117C22×C14911yescharacteristic
328C2×#117C22×C14911yescharacteristic
329C22×C42C22×C14911yescharacteristic
330#421—22no—
331#421C4×C14914yescomplemented
332C2×#104—22no—
333#419—21no—
334#418—21no—
335#417—22no—
336#416—22no—
337#391—21no—
338#390—21no—
339#389—22no—
340#386—22no—
341#385—22no—
342C4×C4⋊C4—22no—
343C4×C22⋊C4—22no—
344#339—22no—
345H(3,ℤ/4)—22no—
346#336—22no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41C2×C4×C14912yes—
358C2×#41Q8×C14912yes—
359C22×Q8D4×C14911yescharacteristic
360C22×D4—21no—
361C22×D4D4×C14911yescharacteristic
362C23×C4—21no—
363C23×C4D4×C14912yes—
364C23×C4C23×C14911yescharacteristic
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16C2×C4×C14912yes—
377C22×C8—21no—
378C22×C8D4×C14912yes—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117C2×C4×C14912yes—
390#117D4×C14912yes—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4D4×C14912yes—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42D4×C14912yes—
407C2×C42D4×C14912yes—
408#104—28no—
409#103—24no—
410#102—24no—
411#95—24no—
412#95—24no—
413C24—21no—
414C24C2×D4×C14911yescharacteristic
415#41—22no—
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—41no—
424#41—41no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C4⋊C4×C14912yescomplemented
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4C4⋊C4×C14912yescomplemented
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—44no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4C22×C4×C14911yescharacteristic
464C22×C4C2×D4×C14911yescharacteristic
465C22×C4C2×D4×C14911yescharacteristic
466C22×C4C2×D4×C14911yescharacteristic
467C22×C4C2×D4×C14911yescharacteristic
468C22×C4C2×D4×C14911yescharacteristic
469C22×C4C2×D4×C14911yescharacteristic
470C22×C4C2×Q8×C14911yescharacteristic
471C22×C4#41×C14911yescharacteristic
472C22×C4#41×C14911yescharacteristic
473C22×C4#41×C14911yescharacteristic
474C22×C4#41×C14911yescharacteristic
475C22×C4#41×C14911yescharacteristic
476C22×C4#41×C14911yescharacteristic
477M16—22no—
478M16—22no—
479M16—41no—
480M16—41no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—41no—
490C2×C8—41no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—48no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—48no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—22no—
506C42—22no—
507C42—22no—
508C42—41no—
509C42—41no—
510C42—41no—
511C42—41no—
512C42—41no—
513C42—41no—
514C42C22⋊C4×C14914yescomplemented
515C23—22no—
516C23—42no—
517C23—44no—
518C23—41no—
519C23—41no—
520C23C4×D4×C14911yescharacteristic
521C23#120×C14911yescharacteristic
522C23#120×C14911yescharacteristic
523C23#121×C14911yescharacteristic
524C23#121×C14911yescharacteristic
525C23C22⋊Q8×C14911yescharacteristic
526C23#124×C14911yescharacteristic
527Q8—22no—
528Q8—22no—
529Q8—41no—
530Q8—41no—
531D4—22no—
532D4—22no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—41no—
538D4—41no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—44no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4C2×C22⋊C4×C14911yescharacteristic
560C2×C4C2×C4⋊C4×C14911yescharacteristic
561C2×C4#117×C14911yescharacteristic
562C2×C4C4×D4×C14911yescharacteristic
563C2×C4C4×D4×C14911yescharacteristic
564C2×C4C4×D4×C14911yescharacteristic
565C2×C4#120×C14911yescharacteristic
566C2×C4#121×C14911yescharacteristic
567C2×C4#121×C14911yescharacteristic
568C2×C4#121×C14911yescharacteristic
569C2×C4#121×C14911yescharacteristic
570C2×C4#121×C14911yescharacteristic
571C2×C4#121×C14911yescharacteristic
572C2×C4C22⋊Q8×C14911yescharacteristic
573C2×C4C22⋊Q8×C14911yescharacteristic
574C2×C4C22⋊Q8×C14911yescharacteristic
575C2×C4C22⋊Q8×C14911yescharacteristic
576C2×C4C22⋊Q8×C14911yescharacteristic
577C2×C4#123×C14911yescharacteristic
578C2×C4#123×C14911yescharacteristic
579C2×C4#123×C14911yescharacteristic
580C2×C4#123×C14911yescharacteristic
581C2×C4#123×C14911yescharacteristic
582C2×C4#124×C14911yescharacteristic
583C2×C4#124×C14911yescharacteristic
584C2×C4#126×C14911yescharacteristic
585C2×C4#126×C14911yescharacteristic
586C2×C4#127×C14911yescharacteristic
587C8—42no—
588C8—42no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—44no—
597C22—42no—
598C22—82no—
599C22—82no—
600C22#385×C14911yescharacteristic
601C22#386×C14911yescharacteristic
602C22#388×C14911yescharacteristic
603C22#392×C14911yescharacteristic
604C22#393×C14911yescharacteristic
605C22#394×C14911yescharacteristic
606C22#396×C14911yescharacteristic
607C4—44no—
608C4—42no—
609C4—44no—
610C4—82no—
611C4—82no—
612C4#380×C14911yescharacteristic
613C4#385×C14911yescharacteristic
614C4#388×C14911yescharacteristic
615C4#390×C14911yescharacteristic
616C4#394×C14911yescharacteristic
617C4#396×C14911yescharacteristic
618C4#397×C14911yescharacteristic
619C4#399×C14911yescharacteristic
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—82no—
627C2#1439×C14911yescharacteristic
628C2#2010×C14912yes—
subgroupG/H
centerC2×C4×C149#127
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
socleC22×C149#392
prime radicalC22×#41×C149C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C149 ◁ C23×C4×C149 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #2296×C149C2semidirect
5. #1733×C149C2semidirect
6. C2×H(3,ℤ/4)×C149C2semidirect
7. #1728×C149C2semidirect
16. #421×C149C4semidirect
121. C2×Q8×C149C4⋊C4semidirect
133. C2×D4×C149C4⋊C4semidirect
199. C42×C149C22⋊C4semidirect
314. #11083C149direct (N × H)
315. C149#11083direct (N × H)
319. #2296C2×C149semidirect
320. #1733C2×C149semidirect
321. C2×H(3,ℤ/4)C2×C149semidirect
322. #1728C2×C149semidirect
331. #421C4×C149semidirect
436. C2×Q8C4⋊C4×C149semidirect
448. C2×D4C4⋊C4×C149semidirect
514. C42C22⋊C4×C149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#421×C1492
#2896×C1492
#2297×C1492
#2296×C1492
#1733×C1492
C2×H(3,ℤ/4)×C1492
#1728×C1492
#11083149